Cartesian coordinate system

A system for locating points by signed distances along mutually perpendicular axes measured from a shared origin. Coordinates specify each point relative to those axes.

Coordinate: A numerical value that specifies a position relative to a chosen reference system. Each coordinate records a point’s signed distance along one axis.
Cartesian coordinates: An ordered list of signed distances locating a point relative to perpendicular coordinate axes. These values are the system’s direct numerical description of a point.
Analytic geometry: The study of geometric objects using algebraic equations and coordinates. It uses Cartesian positions to translate geometric questions into algebra.
Polar coordinate system: A two-dimensional coordinate system that locates points by distance and angle from a fixed origin. Its radial and angular measurements can simplify problems with circular symmetry.
Origin (mathematics): The reference point assigned zero coordinates in a coordinate system. All axis measurements begin at the shared zero point.
Coordinate transformation: A rule for expressing positions or quantities in a different coordinate system. Changing axes or origin changes coordinates without moving the represented point.
Cartesian plane: A two-dimensional plane equipped with two perpendicular coordinate axes and a shared origin. It is the standard setting for plotting points and graphs in two dimensions.
Cylindrical coordinate system: A three-dimensional coordinate system using radial distance, angle, and height. It extends polar coordinates with height for problems organized around an axis.
Coordinate axis: A directed reference line used to measure position in a coordinate system. Perpendicular axes provide the directions in which coordinates are measured.
Distance formula: A formula for finding the straight-line distance between points from their coordinates. Coordinate differences yield geometric distance through the Pythagorean theorem.

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